Staff View: Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay

Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay

In this study, we address a Cauchy problem within the context of the one-dimensional Timoshenko system, incorporating a distributed delay term. The heat conduction aspect is described by the Lord-Shulman theory. Our demonstration establishes that the dissipation resulting from the coupling of the Ti...

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Main Authors:	Choucha A., Boulaaras S., Jan R., Alnegga M.
Other Authors:	57216493937
Format:	Article
Published:	Walter de Gruyter GmbH 2025
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id	my.uniten.dspace-37152
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spelling	my.uniten.dspace-371522025-03-03T15:48:02Z Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay Choucha A. Boulaaras S. Jan R. Alnegga M. 57216493937 36994353700 57205596279 57194856346 In this study, we address a Cauchy problem within the context of the one-dimensional Timoshenko system, incorporating a distributed delay term. The heat conduction aspect is described by the Lord-Shulman theory. Our demonstration establishes that the dissipation resulting from the coupling of the Timoshenko system with Lord-Shulman?s heat conduction is sufficiently robust to stabilize the system, albeit with a gradual decay rate. To support our findings, we convert the system into a first-order form and, utilizing the energy method in Fourier space, and derive point wise estimates for the Fourier transform of the solution. These estimates, in turn, provide evidence for the slow decay of the solution. ? 2024 the author(s), Final 2025-03-03T07:48:02Z 2025-03-03T07:48:02Z 2024 Article 10.1515/dema-2023-0143 2-s2.0-85187115361 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85187115361&doi=10.1515%2fdema-2023-0143&partnerID=40&md5=fef74db836b55f6245c1d68f2d543d9f https://irepository.uniten.edu.my/handle/123456789/37152 57 1 20230143 All Open Access; Gold Open Access Walter de Gruyter GmbH Scopus
institution	Universiti Tenaga Nasional
building	UNITEN Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Tenaga Nasional
content_source	UNITEN Institutional Repository
url_provider	http://dspace.uniten.edu.my/
description	In this study, we address a Cauchy problem within the context of the one-dimensional Timoshenko system, incorporating a distributed delay term. The heat conduction aspect is described by the Lord-Shulman theory. Our demonstration establishes that the dissipation resulting from the coupling of the Timoshenko system with Lord-Shulman?s heat conduction is sufficiently robust to stabilize the system, albeit with a gradual decay rate. To support our findings, we convert the system into a first-order form and, utilizing the energy method in Fourier space, and derive point wise estimates for the Fourier transform of the solution. These estimates, in turn, provide evidence for the slow decay of the solution. ? 2024 the author(s),
author2	57216493937
author_facet	57216493937 Choucha A. Boulaaras S. Jan R. Alnegga M.
format	Article
author	Choucha A. Boulaaras S. Jan R. Alnegga M.
spellingShingle	Choucha A. Boulaaras S. Jan R. Alnegga M. Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay
author_sort	Choucha A.
title	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay
title_short	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay
title_full	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay
title_fullStr	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay
title_full_unstemmed	Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay
title_sort	decay rate of the solutions to the cauchy problem of the lord shulman thermoelastic timoshenko model with distributed delay
publisher	Walter de Gruyter GmbH
publishDate	2025
_version_	1826077362499878912
score	13.244413

Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay

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